Hunting for New Physics with AI-Designed Colliders

Author: Denis Avetisyan

Researchers are leveraging artificial intelligence to create more effective ways to detect subtle signs of physics beyond the Standard Model in particle collider experiments.

A learned observable, derived from an analysis of <span class="katex-eq" data-katex-display="false">e^+e^- \to Z(\to\mu^-\mu^+)H</span> events at <span class="katex-eq" data-katex-display="false">\sqrt{s} = 250</span> GeV, more faithfully compresses information from the collision-demonstrated by its monotonic relationship with the per-event score-than traditional observables such as <span class="katex-eq" data-katex-display="false">O_2 = \sin(2\phi^*)</span> (with <span class="katex-eq" data-katex-display="false">\epsilon \sim eq 0.059</span>) or <span class="katex-eq" data-katex-display="false">O_4 = f_{\rm ext}</span> (<span class="katex-eq" data-katex-display="false">\epsilon \sim eq 0.102</span>). — A learned observable, derived from an analysis of $e^+e^- \to Z(\to\mu^-\mu^+)H$ events at $\sqrt{s} = 250$ GeV, more faithfully compresses information from the collision-demonstrated by its monotonic relationship with the per-event score-than traditional observables such as $O_2 = \sin(2\phi^*)$ (with $\epsilon \sim eq 0.059$ ) or $O_4 = f_{\rm ext}$ ( $\epsilon \sim eq 0.102$ ).

This paper demonstrates the use of AI-driven symbolic regression to discover compact, information-efficient observables for interference measurements at colliders.

Designing optimal observables for precision collider physics is often hampered by the difficulty of obtaining compact analytic forms suitable for probing subtle new physics. In the work ‘AI-Driven Discovery of Information-Efficient Collider Observables for Interference Measurements’, we demonstrate that interpretable, event-level observables can be automatically discovered using AI-driven symbolic evolution guided by Fisher information from matrix-element reweighting. This approach successfully identifies compact analytic functions-recovering characteristic helicity-interference harmonics in both associated production $e^+e^-\to Z(\to μ^-μ^+)H$ and four-lepton decay $pp\to H\to ZZ^*\to e^-e^+μ^-μ^-$ -that outperform standard angular baselines. Could this recast the design of sensitive collider probes as a symbolic discovery problem, paving the way for more efficient and interpretable searches for physics beyond the Standard Model?

Unveiling the Subtleties: Charting a Course Beyond the Standard Model

The Standard Model of particle physics, while remarkably successful, leaves several questions unanswered, necessitating stringent tests of its predictions. Central to these tests are precise measurements of the Higgs boson’s interactions – how it connects to other particles and itself. The Higgs boson, responsible for conferring mass, doesn’t just exist; the way it interacts dictates whether the Standard Model is a complete picture or merely an approximation of a deeper reality. Any deviation from predicted interaction strengths – even minuscule ones – could signal the presence of new particles or forces beyond those currently known. Researchers are therefore focused on meticulously mapping these interactions, employing advanced detectors and data analysis techniques to tease out subtle signals amidst the complex backdrop of particle collisions, hoping to reveal cracks in the Standard Model and guide the development of new theoretical frameworks.

The search for physics beyond the Standard Model often hinges on detecting minute discrepancies between theoretical predictions and experimental results, and discerning violations of Charge-Parity (CP) symmetry is a particularly compelling avenue. CP symmetry, if precisely maintained, implies that a process occurs with the same probability as its mirror image, but many theories proposing solutions to outstanding puzzles – such as the matter-antimatter asymmetry in the universe – predict subtle CP violations. However, these predicted deviations are often incredibly small, demanding the development of ‘observables’ – measurable quantities – with extraordinary sensitivity. These observables must be carefully chosen to maximize the signal from potential new physics while minimizing interference from known, and often much larger, background processes. The challenge lies not simply in building more powerful detectors, but in crafting these sensitive probes that can tease out the faint whispers of physics beyond what is currently understood, effectively amplifying the signal above the noise inherent in high-energy particle collisions.

Extracting precise signals of new physics from particle collisions is hampered by the sheer complexity of the backgrounds – the overwhelming cascade of standard model processes that mimic the sought-after interactions. Current analytical techniques, when applied to the decay of the Z boson into four leptons – a relatively clean final state – only achieve a Fisher Information Efficiency of 0.059. This signifies that less than 6% of the potential statistical power available in the data is being effectively utilized to discern subtle deviations from theoretical predictions. Consequently, identifying rare signals, particularly those violating CP symmetry which could reveal new sources of particle asymmetry, demands innovative approaches to data analysis and significantly enhanced statistical sensitivity. Overcoming this limitation is crucial for fully exploiting the discovery potential of experiments like the Large Hadron Collider.

Analysis of <span class="katex-eq" data-katex-display="false">\sin(\phi_1^<i> + \phi_2^</i>)</span> and <span class="katex-eq" data-katex-display="false">O_{4\ell}</span> interference distributions in <span class="katex-eq" data-katex-display="false">pp \to H \to ZZ^* \to e^{-}e^{+}\mu^{-}\mu^{+}</span> demonstrates significantly improved Fisher information efficiency, increasing from approximately <span class="katex-eq" data-katex-display="false">2.3 \times 10^{-4}</span> to <span class="katex-eq" data-katex-display="false">1.9 \times 10^{-2}</span>, due to clearer separation of opposite-sign interference regions. — Analysis of $\sin(\phi_1^<i> + \phi_2^</i>)$ and $O_{4\ell}$ interference distributions in $pp \to H \to ZZ^* \to e^{-}e^{+}\mu^{-}\mu^{+}$ demonstrates significantly improved Fisher information efficiency, increasing from approximately $2.3 \times 10^{-4}$ to $1.9 \times 10^{-2}$ , due to clearer separation of opposite-sign interference regions.

Constructing Optimal Observables: A Refined Approach to Signal Isolation

Observable construction in experimental physics seeks to reduce the dimensionality of event data by mapping multiple kinematic variables – such as particle momenta, energies, and angles – into a single, scalar quantity. This compression is not arbitrary; the goal is to maximize the observable’s sensitivity to a specific physical process or signal while minimizing its response to background noise. Effectively, the process aims to isolate the relevant information contained within the numerous input variables into a single, easily measurable value, thereby improving statistical power and the ability to detect weak signals. The resulting observable represents a condensed representation of the underlying event, facilitating analysis and interpretation.

Laboratory-frame mappings are crucial preprocessing steps in data analysis, converting initially recorded event data – typically momenta and energies of detected particles – into a coordinate system directly observable and interpretable by physicists. These mappings, often linear transformations, serve to simplify complex relationships between kinematic variables and highlight features sensitive to the underlying physics. Raw data, expressed in the detector’s native frame, may obscure subtle signals due to geometric distortions or the mixing of correlated variables; laboratory-frame mappings address these issues by projecting the data onto a new basis, optimizing signal visibility and reducing dimensionality for subsequent analysis. The choice of mapping is dependent on the specific physics goals and the characteristics of the detector setup, but consistently aims to maximize the information content of the observable.

The interference kernel is a mathematical function central to the construction of sensitive observables in particle physics. It quantifies the interference between different quantum amplitudes contributing to a specific decay or scattering process. This interference is crucial because it introduces sensitivity to subtle physics beyond simple leading-order effects; without accurately modeling this interference, observables will exhibit reduced power to discriminate between signal and background. The kernel’s form is typically derived from the underlying quantum mechanical calculations and depends on the specific kinematic variables used to define the observable; its proper construction requires a complete understanding of the relevant decay topologies and associated amplitudes, often involving complex $2 \rightarrow 2$ or $2 \rightarrow n$ processes.

The sensitivity of an observable is directly proportional to the effectiveness of its constituent mapping and kernel functions. Optimized laboratory-frame mappings efficiently reduce dimensionality and highlight signal features within the raw event data, effectively increasing the signal-to-noise ratio. Simultaneously, the interference kernel, when properly constructed, maximizes constructive interference for signal events while minimizing it for background, thereby amplifying the detectable signal strength. This synergistic effect-a well-designed mapping coupled with an optimized interference kernel-allows for the detection of subtle signals that would otherwise be obscured by statistical fluctuations or background noise, ultimately improving the precision of measurements and the discovery potential of experiments.

Automated Discovery with AI: A New Paradigm for Observable Optimization

An AI-driven evolutionary search algorithm is utilized to navigate the extensive space of potential observables for optimal sensitivity. This approach treats observable definitions as a population of individuals subject to selection, mutation, and crossover operations. The algorithm iteratively refines this population, evaluating each observable’s performance against a defined fitness function – in this case, its ability to distinguish a CP-sensitive deformation from the Standard Model. This process allows for the automated identification of observables that may not be intuitively obvious, but which possess strong discriminating power, surpassing the limitations of manual searches and enabling a more comprehensive exploration of the observable landscape.

Symbolic regression is employed as a core component of the observable discovery process to derive concise, analytically-defined expressions from numerical data. Unlike traditional regression methods that seek best-fit parameters within a pre-defined functional form, symbolic regression automatically searches for the most appropriate mathematical equation – incorporating variables, constants, and mathematical operators – to model the relationship between input features and the target variable. This process results in equations that are not only predictive but also inherently interpretable, allowing researchers to understand the underlying physics driving the observed phenomena. The output is typically a $y = f(x_1, x_2, ..., x_n)$ equation, where $y$ is the target variable and $f$ is the discovered analytic function.

Fisher information, utilized as the guiding metric in observable selection, quantifies the amount of information an observable carries regarding a specific parameter – in this case, the CP-sensitive deformation. Mathematically, it is defined as the expected value of the square of the derivative of the log-likelihood function with respect to the parameter of interest $I(\theta) = E[(\frac{\partial}{\partial \theta} \log p(x;\theta))^2]$ . A higher Fisher information value indicates greater sensitivity; small changes in the parameter will result in larger changes in the observable’s distribution, facilitating more precise parameter estimation. This metric is crucial because it allows the algorithm to prioritize observables that maximize information gain regarding the CP-sensitive deformation, improving the efficiency of the search process and the statistical power of subsequent analyses.

Matrix element reweighting is employed to accelerate the calculation of Fisher information within Monte Carlo simulations. This technique avoids the need to generate entirely new simulation ensembles for each candidate observable being evaluated. Instead, existing Monte Carlo events are reweighted based on the ratio of matrix elements calculated using the candidate observable’s operator and the original simulation’s operator. This reweighting efficiently modifies the event distribution to reflect the sensitivity to the parameter of interest, allowing for a statistically relevant estimate of the Fisher information – quantifying the observable’s ability to constrain the CP-sensitive deformation – with significantly reduced computational cost. The Fisher information $I$ is then estimated as the variance of the reweighted observable.

Beyond Current Limits: Charting a Course for Future Colliders

Recent advancements in collider physics demonstrate a substantial leap in measurement sensitivity through the development of optimized observables. These observables are specifically engineered to incorporate crucial helicity structure features, allowing for a more precise extraction of signal from background noise. This innovative approach achieves a Fisher Information Efficiency of up to 0.102, significantly exceeding the capabilities of traditional measurement techniques. Such heightened sensitivity promises to unlock new opportunities for detailed investigations into fundamental particle interactions, particularly within the Higgs sector, and will be instrumental in maximizing the discovery potential of future high-energy colliders.

The pursuit of a deeper understanding of the Higgs sector necessitates increasingly precise measurements at future colliders, and recent advancements in observable optimization are poised to deliver exactly that. Enhanced sensitivity, achieved through the incorporation of key helicity structure features, will allow physicists to map the Higgs boson’s properties-such as its mass, spin, and couplings to other particles-with unprecedented detail. This improved precision isn’t merely incremental; it opens the door to detecting subtle deviations from the Standard Model, potentially revealing new physics beyond $W$ and $Z$ bosons, and offering clues about dark matter or other yet-undiscovered particles interacting with the Higgs field. Ultimately, this capability will be crucial for determining if the Higgs boson is truly an elementary particle or a composite entity, and for solidifying-or overturning-current understandings of electroweak symmetry breaking.

The development of artificial intelligence techniques is revolutionizing the search for new physics by enabling the discovery of optimized observables previously inaccessible through conventional methods. Rather than relying on pre-defined quantities, this AI-driven framework autonomously explores a vast landscape of potential measurements, identifying those most sensitive to specific theoretical signals. This process not only enhances the precision with which physicists can probe phenomena like the Higgs sector, but also allows for the tailoring of experimental strategies to address particular research goals. The resulting observables, crafted by the AI, often exhibit unique sensitivities and correlations, potentially revealing subtle effects hidden within standard measurements and opening avenues for discoveries beyond the current limits of particle physics.

Analysis employing a selection criterion of $|O_{4l}| > 0.05$ demonstrates a substantial enhancement in measurement precision. Specifically, the asymmetry signal, $S_{asym}$ , gains a factor of 1.30 when normalized by the square root of the data sample size, $\sqrt{DSM}$ . Furthermore, the purity of the asymmetry measurement itself experiences a marked improvement, increasing by a factor of 2.25 relative to standard measurement techniques. These gains indicate a considerable leap forward in the ability to discern subtle signals within collider data, paving the way for more precise investigations into fundamental particle interactions and properties.

The pursuit of information-efficient collider observables, as detailed in this study, echoes a fundamental principle of elegant design: achieving maximum impact with minimal complexity. The AI’s capacity to distill intricate physical phenomena into compact, interpretable expressions is reminiscent of a skilled artisan refining a design until only the essential elements remain. Søren Kierkegaard observed, “Life can only be understood backwards; but it must be lived forwards.” This resonates with the research; physicists traditionally ‘understood’ observables through forward modeling, while this work ‘lives’ forward by letting the AI discover optimal observables from data, ultimately revealing a deeper, more concise understanding of the underlying physics. The resulting observables aren’t merely functional; they possess an inherent poetic quality, whispering insights into potential deviations from the Standard Model.

Beyond the Signal

The pursuit of new physics at colliders has long resembled a delicate balancing act-maximizing sensitivity while minimizing statistical burden. This work suggests a shift in approach: not merely designing observables, but evolving them. The elegance of discovering concise, interpretable expressions via symbolic regression is not simply a technical achievement; it hints at a deeper harmony between mathematical form and physical reality. One anticipates that future iterations will move beyond single observable optimization, exploring landscapes of correlated measurements-a compositional approach, not a chaotic accumulation of data.

However, the current methodology, while promising, remains tethered to specific kinematic regimes and idealized detector responses. The true test will lie in its adaptability to realistic, complex environments-and its ability to unearth genuinely novel observables, rather than simply re-discovering known quantities in a different guise. The question isn’t just whether an algorithm can find a signal, but whether it can reveal a physics previously obscured by the limitations of human intuition.

Ultimately, this work underscores a fundamental principle: beauty scales, clutter does not. The drive toward information-efficient observables is not merely a matter of statistical optimization; it is an aesthetic imperative. The future likely holds a synthesis of analytic insight and algorithmic exploration, a collaborative dance between human ingenuity and machine precision-a search for the most concise and revealing language in which to describe the universe.

Original article: https://arxiv.org/pdf/2605.14783.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

Unveiling the Subtleties: Charting a Course Beyond the Standard Model

Constructing Optimal Observables: A Refined Approach to Signal Isolation

Automated Discovery with AI: A New Paradigm for Observable Optimization

Beyond Current Limits: Charting a Course for Future Colliders

Beyond the Signal

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